Degree Conditions for Graphs to Have Spanning Trees with Few Branch Vertices and Leaves
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A leaf of a tree is a vertex of degree one and a branch vertex of a tree is a vertex of degree strictly greater than two. This paper shows two degree conditions for graphs to have spanning trees with total bounded number of branch vertices and leaves. Moreover, the sharpness of our results is shown.
KeywordsSpanning tree Branch vertex Leaf Fan-type degree condition